Geometrical understanding of the PCA subspace method for overdetermined blind source separation

In this paper, we discuss approaches for blind source separation where we can use more sensors than the number of sources for a better performance. The discussion focuses mainly on reducing the dimension of mixed signals before applying independent component analysis. We compare two previously proposed methods. The first is based on principal component analysis, where noise reduction is achieved. The second involves selecting a subset of sensors based on the fact that a low frequency prefers a wide spacing and a high frequency prefers a narrow spacing. We found that the PCA-based method behaves similarly to the geometry-based method for low frequencies in the way that it emphasizes the outer sensors and yields superior results for high frequencies, which provides a better understanding of the former method.